Trip Generation & Gravity Model
Gabriel Barrett-Jackson, Matt Khinda, Samantha Page
March 10, 2023
We ran linear regression models using the following variables:
- Log-base 2 transformation of median income (in thousands)
- Presence of children in the household
- Homeownership
- Households with residents age 65 or older
##
## Call:
## lm(formula = HBO_trips ~ log2(inc_k) + any_kids + homeownership +
## age_65, data = okc_hhs)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.6917 -1.6957 -0.6649 0.9922 13.3083
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.3884 1.3996 -0.277 0.782042
## log2(inc_k) 0.4691 0.2409 1.947 0.054659 .
## any_kidsTRUE 2.8389 0.8240 3.445 0.000868 ***
## homeownershipTRUE 0.2548 0.7696 0.331 0.741327
## age_65TRUE 1.4842 0.7242 2.049 0.043328 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.963 on 90 degrees of freedom
## (10 observations deleted due to missingness)
## Multiple R-squared: 0.1814, Adjusted R-squared: 0.145
## F-statistic: 4.986 on 4 and 90 DF, p-value: 0.001123For home-based other trip productions, income, presence of children, and adults over 65 were significant variables in the regression.
##
## Call:
## lm(formula = HBW_trips ~ log2(inc_k) + any_kids + homeownership +
## age_65, data = okc_hhs)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.7806 -0.9418 -0.4117 0.6475 3.5883
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.3299 0.6247 0.528 0.5988
## log2(inc_k) 0.1269 0.1075 1.180 0.2412
## any_kidsTRUE 0.2396 0.3678 0.651 0.5165
## homeownershipTRUE 0.2657 0.3435 0.773 0.4413
## age_65TRUE -0.7322 0.3232 -2.265 0.0259 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.323 on 90 degrees of freedom
## (10 observations deleted due to missingness)
## Multiple R-squared: 0.1063, Adjusted R-squared: 0.06661
## F-statistic: 2.677 on 4 and 90 DF, p-value: 0.03675For home-based work trip productions, only the presence of residents over 65 was significant.
##
## Call:
## lm(formula = NHB_trips ~ log2(inc_k) + any_kids + homeownership +
## age_65, data = okc_hhs)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.1619 -1.7226 -0.5404 1.3712 9.7052
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.82175 1.26218 1.443 0.152397
## log2(inc_k) 0.06942 0.21728 0.320 0.750072
## any_kidsTRUE 2.92598 0.74306 3.938 0.000162 ***
## homeownershipTRUE 0.27665 0.69402 0.399 0.691118
## age_65TRUE -0.87913 0.65306 -1.346 0.181630
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.672 on 90 degrees of freedom
## (10 observations deleted due to missingness)
## Multiple R-squared: 0.2006, Adjusted R-squared: 0.1651
## F-statistic: 5.645 on 4 and 90 DF, p-value: 0.0004227For non-home-based trip productions, only the presence of children was a significant variable in the regression.
As expected, attractions and productions are primarily concentrated in the downtown area–attractions even more so than productions. Both generally follow the density maps of residences and employment that we created earlier in the semester.
Average travel time by trip purpose (based on NHTS data)
By summarizing the NHTS trips by purpose we found that Home-Based Work trips had the longest average travel time of 26.45 minutes, while both Home-Based Other and Non-Home-Based trips were significantly shorter with average times of 17.15 and 16.33 minutes respectively. This seems accurate because residents are typically more willing to travel farther to their jobs than for other day-to-day purposes.
Esitmating travel flows using an exponential deterrence function
Based on the observed values from NHTS data, we calibrated our exponential deterrence function to best fit those travel times. We decided to use an exponential deterrence function in keeping with our expontential accessibility decay function which reflects the same assumed value of travel time. The exponential function is written as: \[\begin{equation} F_{ijp} = e^{-mt_{ij}} \end{equation}\] where \(F_{ij}\) is the friction factor for trips with purpose p between zone i and zone j, \(t_{ij}\) is the the travel time from zone i to zone j. We adjusted the m value for each purpose. For Home-Based Work trips we used a value -0.06, for Home-Based Other trips we used a value of -0.18, and for Non-Home-Based trips we used a value of -0.2. The resulting estimates were all within .2 minutes of the NHTS averages.
## # A tibble: 3 × 4
## purpose nhts_avg_time pred_time time_dif
## <chr> <dbl> <dbl> <dbl>
## 1 HBO 17.2 17.0 0.157
## 2 HBW 26.5 26.5 -0.0744
## 3 NHB 16.3 16.1 0.197Visualizing travel flows by purpose and county
To better understand trip distribution within the MSA, we mapped the most frequent (250+) origin-destination pairs by trip type. We noticed that Home-Based Other trips are the most spatially distributed across the region, while Home-Based Work trips were the most concentrated — particularly around what we believe to be the major employment centers just south of Oklahoma City. We also created three chord diagrams showing the intra- and inter-county flows by trip purpose. This allows us to better understand which counties are more attractive or productive for each trip purpose.
Home-Based Other flows
Home-Based Work flows
Non-Home Based flows
